8 3 Compound Interest Present Value of Compound

Key Terms Present Value: the principal that would have to be invested now to

Formulas 1)PV = A/(1+i)^n 2)PV = A(1+i)^-n PV is the present value A is

Example 1 Jamar is investing $3500. 00 and he would like it to grow

Solution 1 PV=A/(1+i)^n 3500=8000/(1+i)^15 3500(1+i)^15=8000 (1+i)^15=2. 29 1+i=1. 0567 i=0. 0567 i=5. 67% ∴

Example 2 Jade borrowed money so that she could buy a car on her

Solution 2 PV=A(1+i)^-n PV=58000(1+0. 034)^-14 PV=58000(1. 034)^14 PV=36319. 55 Remember Jade paid $3580. 00

Question 1 Bobby wants $10000. 00 in 4 years for his first year of

Solution Using the Formula: PV = A(1+i)^-n PV = 10000(1+0. 07)^-4 PV = 10000(1.

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8. 3 Compound Interest Present Value of Compound Interest

Key Terms Present Value: the principal that would have to be invested now to get a specific future value in a certain amount of time. PV is used for present value instead of P, since P is used for principal. Compound Interest: Interest that is added to the principal before new interest earned is calculated. So interest is calculated on the principal and on interest already earned. Interest is paid at regular time intervals called the compounding period. Compounding period: is number of intervals at which interest is calculated. Note Annually- 1 time per year Semi-annually – 2 times per year Quarterly – 4 times per year Monthly – 12 times per year

Formulas 1)PV = A/(1+i)^n 2)PV = A(1+i)^-n PV is the present value A is the future value I is the interest rate N is the number of compound periods

Example 1 Jamar is investing $3500. 00 and he would like it to grow to$8000 in 15 years. At what annual interest rate, compounded annually will give him the $8000. Given: PV=2500 A=8000 N=15 Need to find: I=?

Solution 1 PV=A/(1+i)^n 3500=8000/(1+i)^15 3500(1+i)^15=8000 (1+i)^15=2. 29 1+i=1. 0567 i=0. 0567 i=5. 67% ∴ At a interest rate of 5. 67%/a, Jamar will have $8000. 00 in 15 years.

Example 2 Jade borrowed money so that she could buy a car on her 21 st birthday. She paid $3580 as a down payment and the interest rate was 6. 8%/a compounded semi-annually. On her 28 th birthday she paid her loan and paid a total of $58000. How much did Jade buy the car for? Given: A=58000. 00 I=0. 034 N=14 Need to find: PV=?

Solution 2 PV=A(1+i)^-n PV=58000(1+0. 034)^-14 PV=58000(1. 034)^14 PV=36319. 55 Remember Jade paid $3580. 00 as a down payment. Price of Car=36319. 55+3580. 00 Price of Car=39899. 55 ∴The price of the car was $39899. 55

Question 1 Bobby wants $10000. 00 in 4 years for his first year of university. The interest rate is 7%/a on his investment. How much money should Bobby invest now, so that in 4 years he will have $10000. 00? Given: I=0. 07 A=10000. 00 N=4 Need to find: PV=?

Solution Using the Formula: PV = A(1+i)^-n PV = 10000(1+0. 07)^-4 PV = 10000(1. 07)^-4 PV = 10000(0. 7628952) PV = 7628. 95 ∴ Bobby should invest approximately $7628. 95 so that in 4 years he will have $10000.